[The discount rate gives the degree of patience of people involved.] Now, this is the time to use the boundary conditions to find some meaningful interpretations. To understand social science models, we have to simplify some of the assumptions first, and see how things behave in this ‘simpler’ and ‘idealized’ models. Then we can project these results into more chaotic world. This writer has neither such intellectual capability nor time to pursue it in that dimension, so I leave it to the readers to think about that case. It is scientific tradition, including in Physics and other disciplines, to consider any phenomenon with that approach, for example, earlier analysis in Physics always assumed frictionless environment to study velocities and speed in an environment. So, in a somewhat simplified world, let’s assume both the king and the PCM have same discount rate, i.e. r1=r2. I have also advised in our previous discussion that parties be more resolute, so q2>q1. This also mean that they are the one for whom G2(0)=0.